2008 AIME I Problems/Problem 2
Problem
Square has sides of length units. Isosceles triangle has base , and the area common to triangle and square is square units. Find the length of the altitude to in .
Solution 1
Note that if the altitude of the triangle is at most , then the maximum area of the intersection of the triangle and the square is . This implies that vertex G must be located outside of square .
Let meet at and let meet at . Clearly, since the area of trapezoid is . Also, .
Let the height of be . By the similarity, , we get . Thus, the height of is .
See also
2008 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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this could have been a #1-#5 on the amc 10 lol